\(3\)-isogeny Selmer groups and ranks of abelian varieties in quadratic twist families over a number field
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Publication:2280563
DOI10.1215/00127094-2019-0031zbMath1442.14084arXiv1709.09790OpenAlexW3098079019MaRDI QIDQ2280563
Manjul Bhargava, Ari Shnidman, Robert J. Lemke Oliver, Zev Klagsbrun
Publication date: 18 December 2019
Published in: Duke Mathematical Journal (Search for Journal in Brave)
Full work available at URL: https://arxiv.org/abs/1709.09790
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Cites Work
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- Generalized Heegner cycles at Eisenstein primes and the Katz \(p\)-adic \(L\)-function
- Arithmetic invariant theory and 2-descent for plane quartic curves. With an appendix by Tasho Kaletha
- Disparity in Selmer ranks of quadratic twists of elliptic curves
- On the ranks of the 2-Selmer groups of twists of a given elliptic curve
- Binary quartic forms having bounded invariants, and the boundedness of the average rank of elliptic curves
- Computing the Selmer group of an isogeny between Abelian varieties using a further isogeny to a Jacobian
- Groupes de Selmer et corps cubiques. (Selmer group and cubic fields)
- Rank-one twists of a certain elliptic curve
- Twists and reduction of an elliptic curve
- The size of Selmer groups for the congruent number problem. II. With an appendix by P. Monsky.
- Computing a Selmer group of a Jacobian using functions on the curve
- Class groups and Selmer groups
- Elements of given order in Tate-Shafarevich groups of abelian varieties in quadratic twist families
- Ternary cubic forms having bounded invariants, and the existence of a positive proportion of elliptic curves having rank 0
- Elliptic curves with a lower bound on 2-Selmer ranks of quadratic twists
- Quadratic twists of abelian varieties and disparity in Selmer ranks
- Note on the rank of quadratic twists of Mordell equations
- Good reduction of abelian varieties
- The Diophantine equation \(ax^3+by^3+cz^3=0\)
- A Markov model for Selmer ranks in families of twists
- Quadratic twists of elliptic curves with 3-Selmer rank 1
- Descent via (3,3)-isogeny on Jacobians of genus 2 curves
- Splitting of Abelian Varieties
- The effect of twisting on the 2-Selmer group
- Elementary 3-descent with a 3-isogeny
- L-series with nonzero central critical value
- Rational points on hyperelliptic curves having a marked non-Weierstrass point
- Arithmetic aspects of the Burkhardt quartic threefold
- Selmer groups as flat cohomology groups
- Quadratic Twists of Abelian Varieties With Real Multiplication
- The average size of the 3‐isogeny Selmer groups of elliptic curves y2=x3+k
- $2$-Selmer groups of hyperelliptic curves with marked points
- Local invariants of isogenous elliptic curves
- Arithmetic invariant theory
- GOLDFELD’S CONJECTURE AND CONGRUENCES BETWEEN HEEGNER POINTS
- Arithmetic on curves of genus 1. VIII. On conjectures of Birch and Swinnerton-Dyer.
